Pound chicken breasts to about 1/2 inch thick. Place in a large ziploc bag or in a container that has an airtight lid for marinating in the fridge. Set aside.
In a mixing bowl, combine the marinade ingredients (yogurt, olive oil, red wine vinegar, garlic, lemons, parsley, oregano, salt, and pepper). Mix well. Pour the marinade over the chicken. Seal and refrigerate for at least 1 hour up to overnight.
When ready to cook the chicken, bring a large pan to medium high heat.
Once pan is very hot, add 1-2 tablespoons of oil.Use tongs to shake excess marinade off each chicken breast, and then place into the hot pan with oil. Sear chicken on each side for 4-5 minutes, until chicken is cooked through.
Once cooked, remove from hot pan and set aside to rest, until ready to slice and put into the salad.(You can also make this Greek Chicken ahead of time and chill it until ready to serve on the salad.) Before serving, slice the chicken and if needed, add a little finishing salt to taste.